#include <bits/stdc++.h>
using namespace std;
#define int long long int
using pi = pair<int, int>;
using vb = vector<bool>;
using vi = vector<int>;
using vvi = vector<vi>;
using vpi = vector<pi>;
using vvpi = vector<vpi>;
const int MAXN = 100'001, MAXM = 200'001;
const int INF = 1e18;
int n, m, X[MAXM], Y[MAXM], C[MAXM];
int S, T, U, V;
vi adj[MAXN], mst_adj[MAXN];
void dijkstra(int u, vi &dist, vi &par) {
dist.assign(n+1, INF);
par.assign(n+1, -1);
dist[u] = 0; par[u] = -1;
priority_queue<pi, vector<pi>, greater<pi>> q;
q.push({0, u});
while (!q.empty()) {
auto cur = q.top();
q.pop();
int cu = cur.second, cdist = cur.first;
for (auto &el : adj[cu]) {
int cv = X[el] == cu ? Y[el] : X[el];
int vdist = C[el];
if(dist[cu] + vdist < dist[cv]) {
par[cv] = cu;
dist[cv] = dist[cu] + vdist;
q.push({dist[cu] + vdist, cv});
}
}
}
}
vi get_topsort(vi &dist, vvi &children) {
children.assign(n+1, vi());
vi deg(n+1, 0);
for (int i = 1; i <= n; i++) {
for (auto &eid : adj[i]) {
int cv = X[eid] == i ? Y[eid] : X[eid], cd = C[eid];
if (dist[cv] + cd != dist[i]) continue;
children[cv].push_back(i);
deg[i]++;
}
}
vi st; for (int i = 1; i <= n; i++) if (deg[i] == 0) st.push_back(i);
vi order;
while (!st.empty()) {
int cur = st.back();
st.pop_back();
for (auto &el : children[cur]) {
deg[el]--;
if (deg[el] == 0) st.push_back(el);
}
order.push_back(cur);
}
return order;
}
signed main() {
cin >> n >> m;
cin >> S >> T >> U >> V;
for (int i = 1; i <= m; i++) {
cin >> X[i] >> Y[i] >> C[i];
adj[X[i]].push_back(i);
adj[Y[i]].push_back(i);
}
vvi dist(n+1, vi());
vvi parents(n+1, vi());
// for (int i = 1; i <= n; i++) {
for (int i : {S, T, U, V}) {
dijkstra(i, dist[i], parents[i]);
}
int stdist = dist[S][T];
vb is_on_sp(n+1, false);
vi on_sp; for (int i = 1; i <= n; i++) {
if (dist[S][i] + dist[T][i] != stdist) continue;
on_sp.push_back(i);
is_on_sp[i] = true;
}
vvi ts1_adj;
vi stop = get_topsort(dist[S], ts1_adj);
vi bestU(n+1, INF), bestV(n+1, INF);
int best = dist[U][V];
for (int i : stop) {
if (!is_on_sp[i]) continue;
bestU[i] = min(bestU[i], dist[U][i]);
bestV[i] = min(bestV[i], dist[V][i]);
for (auto &v : ts1_adj[i]) {
bestU[v] = min(bestU[v], bestU[i]);
bestV[v] = min(bestV[v], bestV[i]);
}
best = min(best, bestU[i] + dist[V][i]);
best = min(best, bestV[i] + dist[U][i]);
}
cout << best;
return 0;
}
